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A solution to the invariant subspace problem on the space \(\ell _ 1\). (English) Zbl 0574.47006

The paper is an addendum to the author’s earlier paper [ibid. 16, 337-401 (1984; Zbl 0566.47003)]. In this note he indicates modifications which yield an operator on the space \(\ell_ 1\) with no proper invariant subspaces. The problem for operators on Hilbert space or reflexive Banach spaces remains open.
Reviewer: R.G.Douglas

MSC:

47A15 Invariant subspaces of linear operators
46A45 Sequence spaces (including Köthe sequence spaces)

Citations:

Zbl 0566.47003
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